The present invention relates to a scanning optical system for forming a laser beam scanning on a scan target surface.
In general, a scanning optical system is employed in, for example, a laser beam printer, a digital copying machine, a laser fax machine and a laser plotter. In such an apparatus, the scanning optical system is used to form a beam spot which is on/off modulated according to image information and which scans on the scan target surface (e.g., a photoconductive drum).
Hereafter, a direction in which a beam spot is scanned on the scan target surface is referred to as a main scanning direction, and a direction perpendicular to the main scanning direction on the scan target surface is referred to as an auxiliary scanning direction. In the following description, the shape of optical elements, directions of power of the optical elements and the like are described with reference to the main and auxiliary scanning directions on the scan target surface. That is, if an optical element is described to have a refractive power in the main scanning direction, the power affects the beam in the main scanning direction on the scan target surface regardless of the orientation of the element.
FIG. 8 shows a configuration of the above mentioned conventional scanning optical system 2. The scanning optical system 2 includes a laser source 70, a line-like image forming optical system 71, a polygonal mirror 72, an imaging optical system 73, and a photoconductive drum 74.
The laser beam emitted by the laser source 70 is converged in the auxiliary scanning direction by the line-like image forming optical system 71 to form a line-like image extending in the main scanning direction in the vicinity of a reflective surface of the polygonal mirror 72 rotating about its rotational axis at a constant angular speed.
The beam emerged from the line-like image forming optical system 71 is dynamically deflected by the polygonal mirror 72 within a predetermined angular range. Then, the imaging optical system 73 converges the deflected laser beam on the scan target surface to form a beam spot scanning in the main scanning direction at a constant speed. Since an outer surface (i.e., the scan target surface) of the photoconductive drum 74 is moved in the auxiliary scanning direction by rotation of the photoconductive drum 74 about its rotational axis, a two dimensional image consisting of a plurality of dots can be formed on the outer surface of the photoconductive drum 74.
Meanwhile, the polygonal mirror 72 is required to be configured such that all of the reflective surfaces thereof are exactly parallel with the rotational axis of the polygonal mirror 72. However, to make all of the reflective surfaces of the polygonal mirror exactly parallel with the rotational axis thereof during manufacturing process of the polygonal mirror is impossible. Therefore, in general, the polygonal mirror 72 includes a so-called facet error in which one or more reflective surfaces slightly tilt with respect to the rotational axis.
The facet error will be explained in detail with reference to FIGS. 9A, 9B and 10. FIG. 9A is a perspective view of the polygonal mirror 72. FIG. 9B is a side view of the polygonal mirror 72 viewed along a line perpendicular to the rotational axis of the polygonal mirror 72. If a reflective surface is tilted with respect to the rotational axis of the polygonal mirror 72 as shown by a broken line in FIG. 9A, a beam reflected by the tilted reflective surface deviates in the auxiliary scanning direction from an ideal optical path as shown by a dashed arrow in FIG. 9B. Consequently, the beam spot is formed at a position shifted in the auxiliary scanning direction form an ideal position on the scan target surface.
To avoid ill effects caused by the facet error, the scanning optical system 2 employs a configuration explained below. FIG. 10 is an optical block diagram of the scanning optical system 2 viewed along a line perpendicular to the auxiliary scanning direction. As shown in FIG. 10, a position of a reflective surface of the polygonal mirror 72 and a position at which the line-like image is formed by the line-like image forming optical system 71 are set substantially consistent with each other. Further, the position of the line-like image and the outer surface of the photoconductive drum 74 (i.e., the scan target surface) are set optically conjugate with each other in the auxiliary scanning direction with respect to the imaging optical system 73.
In FIG. 10, the reflective surface indicated by a solid line 72c shows a situation in which the facet error is not caused, and the reflective surface indicated by a broken line 72d shows a situation in which the facet error is caused. Since the position of the line-like image and the outer surface of the photoconductive drum 74 are set optically conjugate with each other, even if the line-like image is reflected by a tilted reflective surface (72d) of the polygonal mirror 72, an image point of the beam reflected by the tilted reflective surface 72d coincides with an image point of the beam reflected by a normal reflective surface (72c). In FIG. 10, a beam Ld indicated by broken lines is the beam reflected by the tilted reflective surface 72d, and a beam Lc indicated by solid lines is the beam reflected by the normal reflective surface 72c. 
By employing the configuration shown in FIG. 10 to avoid the ill effects of the facet error, the polygonal mirror 72 is not required to be configured such that each reflective surface is exactly parallel with the rotational axis of the polygonal mirror. Accordingly, the manufacturing cost of the scanning optical system 2 can be reduced.
A point at which the beam proceeding toward the polygonal mirror 72 is reflected by a reflective surface of the polygonal mirror 72 is referred to as a “deflection point”. FIG. 11 illustrates a change of the deflection point caused in connection with rotation of the polygonal mirror 72. As shown in FIG. 11, when the polygonal mirror 72 is positioned at a rotational position A0, the beam proceeding toward the polygonal mirror 72 is reflected at a point P0 on the reflective surface 72c. Meanwhile, when the polygonal mirror 72 is positioned at a rotational position A1, the beam proceeding toward the polygonal mirror 72 is reflected at a point P1 on the reflective surface 72c. As a result, the deflection point shifts by a distance d0 along an optical path of the beam proceeding toward the polygonal mirror 72 from the point P0 to the point P1.
Since a deflection angle which is an angle formed between a central axis of the beam proceeding toward the polygonal mirror 72 and a reflective surface of the polygonal mirror changes between the rotational position A0 and the rotational position A1, the change of the deflection point is also considered as a phenomenon caused in connection with a change of the deflection angle.
Such a change of the deflection point inevitably occurs because a distance from a center C of the polygonal mirror 72 to the reflective surface 72c varies depending on positions on the reflective surface 72.
In a case where the position at which the line-like imaged is formed coincides with the point P0, if the polygonal mirror 72 is positioned at the rotational position A1, the position at which the line-like image is formed shifts by the distance d0 with respect to the current deflection point P1. As a result, the conjugate relationship between the position of the line-like image and the outer surface of the photoconductive drum 74 is lost. That is, in actuality, the conjugate relationship holds only at a certain deflection angle.
FIG. 12 is a side view of the scanning optical system 2 illustrating the above mentioned phenomenon of the change of the deflection point. In FIG. 12, a numerical reference 72a indicates a position of the reflective surface of the polygonal mirror when the conjugate relation ship stands (i.e., when the deflection point is positioned at the point P0 in FIG. 11). A numerical reference 72b indicates a position of the reflective surface in a situation where the deflection point is shifted from a proper position 72a. 
A broken line 72e shown at the position 72b indicates a reflective surface of the polygonal mirror 72 tilted due to the facet error. As described above, the conjugate relationship is lost when the deflection point shifts form the proper position 72a. Therefore, when the beam is reflected by the tilted reflective surface 72e at the shifted deflection position 72b, a beam spot of a beam Le reflected by the tilted reflective surface 72e is formed at a position shifted in the auxiliary scanning direction on the scan target surface from an ideal position.
That is, the beam spot of the beam Le shifts from the beam spot of a beam Lc reflected by the normal reflective surface (72c) at the proper deflection position 72a. As a result, a scan line which is a locus of the beam spot on the scan target surface shifts in the auxiliary scanning direction from an ideal position.
Hereafter, such a phenomenon in which the scan line shifts on the scan target surface in the auxiliary scanning direction is referred to as “jitter in the auxiliary scanning direction”. Further, the amount of the jitter in the auxiliary scanning direction is referred to as “jitter amount”.
The jitter amount changes depending on: a lateral magnification of the imaging optical system 73 in the auxiliary scanning direction (m); a tilt angle of a reflective surface of the polygonal mirror with respect to the rotational axis of the polygonal mirror (φ); and a shift amount of the deflection point from the position at which the line-like image is formed (d0). The jitter amount increases as at least one of m, φ and d0 increases.
Foe example, the jitter amount y′ may be defined as:y′=|2md1φ|                where d1 represents the maximum shift amount of the deflection point from the position at which the line-like image is formed.        
Meanwhile, a polygonal mirror has a plurality of reflective surfaces. Therefore, in many cases, tilt angles φ vary among the plurality of reflective surfaces. If the tilt angles φ vary among the plurality of reflective surfaces, the jitter amounts also vary among the plurality of reflective surfaces of the polygonal mirror. In FIG. 13, normal scan lines 89 having no jitter amounts are indicated on the left side, and scan lines 90 having jitter amounts JI which vary among the plurality of reflective surfaces are indicated on the right side.
When such variations of the jitter amounts occur, a jitter pattern PA repeats with rotations of the polygonal mirror. The variations of the jitter amount deteriorate imaging quality. In particular, when a back focus (i.e., a distance between the imaging optical system and the photoconductive drum) is lengthened to downsize a size of an apparatus (for example, a printer) accommodating the scanning optical system and to improve flexibility of mechanical design of the apparatus, the jitter amount increases and thereby the degree of reduction in imaging quality exceeds a permissible amount.
Preferably, the jitter amount is less than or equal to 5.0 μm when the resolution is 600 dpi (dots per inch), although the permissible jitter amount varies depending on resolution dpi. However, there is a case where the jitter amount of the conventional scanning optical system exceeds the permissible jitter amount of 5.0 μm. For example, the jitter amount of a scanning optical system shown in a practical example 4 of Japanese Provisional. Publication NO. HEI7-113950 takes a value of 7.0 μm.
Since, in general, if the number of reflection surfaces is less than or equal to 6 and if the lateral magnification in the auxiliary scanning direction |m|>1.85, the jitter amount produced by a conventional design technique of the scanning optical system exceeds 5.0 μm, which deteriorates the imaging quality considerably.
In Japanese Provisional Publication NO. HEI 5-142495, a configuration of a scanning optical system to avoid an ill effect of an error in which a distance between a rotational axis of a polygonal mirror and each reflective surface of the polygonal mirror varies from one reflective surface to another reflective surface is disclosed. However, the error of the polygonal mirror discussed in this publication is a manufacturing error of the polygonal mirror with regard to the distance between the rotational axis and each reflective surface. Therefore, the error discussed in the publication HEI 5-142495 is different from the above mentioned phenomenon of the change of the deflection point which occurs inevitably.
As described above, a problem caused by the phenomenon of the change of the deflection point (i.e., the variations of the jitter amounts) has not been resolved. One of fundamental solutions to this problem is to reduce the jitter amount by employing a polygonal mirror manufactured with extremely high accuracy.
However, a polygonal mirror manufactured using a typical manufacturing process usually has the facet error of about 180″ (=0.00087 rad). To manufacture a polygonal mirror having precision higher than that of the polygonal mirror manufactured using the typical manufacturing process (i.e., to manufacture a polygonal mirror having the facet error less than 180″) considerably increases the manufacturing cost of the polygonal mirror.